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27
Mixed finite element methods for viscoelastic flow analysis: A review
 J. NonNewtonian Fluid Mech
, 1998
"... The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic visc ..."
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Cited by 55 (3 self)
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The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic viscous stress splitting (EVSS) method as well as the related discrete EVSS and the socalled EVSSG method are discussed among others. Furthermore, stabilization techniques such as the streamline upwind PetrovGalerkin (SUPG) and the discontinuous Galerkin (DG) are reviewed. The performance of the numerical schemes for both smooth and nonsmooth benchmark problems is discussed. Finally, the capabilities of viscoelastic flow solvers to predict experimental observations are reviewed. 1
A survey of computational rheology
 in Proceedings of the XIIIth International Congress on Rheology
, 2000
"... A survey is presented of the field of computational rheology applied to the analysis of viscoelastic effects in complex flows of polymeric fluids. First, I outline the modelling approaches adopted currently in numerical simulations and discuss the role of computational rheology within the general st ..."
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Cited by 19 (0 self)
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A survey is presented of the field of computational rheology applied to the analysis of viscoelastic effects in complex flows of polymeric fluids. First, I outline the modelling approaches adopted currently in numerical simulations and discuss the role of computational rheology within the general study of structured liquids. Developments in the macroscopic and micromacro simulation strategies are then reviewed. Finally, I stress important unsolved problems and offer suggestions for future work.
Peristaltic transport of an OldroydB fluid in a planar channel
 Math. Problems Eng
"... The effects of an OldroydB fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effect ..."
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Cited by 9 (1 self)
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The effects of an OldroydB fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effects of the various parameters of interest on the flow are shown and discussed.
GLOBAL STRONG SOLUTION TO THE DENSITYDEPENDENT INCOMPRESSIBLE VISCOELASTIC FLUIDS
, 905
"... Abstract. The existence and uniqueness of the global strong solution with small initial data to the threedimensional densitydependent incompressible viscoelastic fluids is established. The local existence and uniqueness of the global strong solution with small initial data to the threedimensional ..."
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Cited by 6 (1 self)
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Abstract. The existence and uniqueness of the global strong solution with small initial data to the threedimensional densitydependent incompressible viscoelastic fluids is established. The local existence and uniqueness of the global strong solution with small initial data to the threedimensional compressible viscoelastic fluids is also obtained. A new method is developed to estimate the solution with weak regularity. Moreover, as a byproduct, we show the global existence and uniqueness of strong solution to the densitydependent incompressible NavierStokes equations using a different technique from [8].
Flows of inelastic nonNewtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows
, 2004
"... Abstract. Numerical simulations are presented for flows of inelastic nonNewtonian fluids through periodic arrays of aligned cylinders. The truncated powerlaw fluid model is used for the relationship between the viscous stress and the rateofstrain tensor. Results for the drag coefficient for cree ..."
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Cited by 3 (2 self)
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Abstract. Numerical simulations are presented for flows of inelastic nonNewtonian fluids through periodic arrays of aligned cylinders. The truncated powerlaw fluid model is used for the relationship between the viscous stress and the rateofstrain tensor. Results for the drag coefficient for creeping flows of such fluids have been presented in a companion paper [1]. In this second part the effects of finite fluid inertia are investigated for flows through square arrays. It is shown that the Reynoldsnumber dependence of the drag coefficient of a cylinder in the array is of the form Cd ≡ F/(ηU) = k0 + k2Re2 +.. for small values of the Reynolds number Re ≡ ρaU/η, where F is the drag force, U is the averaged velocity in the array, η = K(U/a)n−1 is a viscosity scale with K and n the powerlaw coefficient and index and a the cylinder radius, and k0 is the drag coefficient for creeping flows. The proportionality constant k2 depends on the way the drag coefficient and the Reynolds number are defined. It is shown that the observed strong dependence of k2 on n can almost be eliminated by using length scales different from a in the viscosity scales η used in the definition of Re and in the definition of the drag coefficient. Numerical simulation results are also presented for the velocity variance components. Results for flows at moderate Reynolds number, of order 100, are also presented; these are qualitatively similar to those for Newtonian fluids. The value of the Reynolds number beyond which the flow becomes unsteady was related to the Newtonian fluid case by rescaling. These results for moderateReynoldsnumber flow are compared against previously published experimental data.
Flows of viscoplastic materials: models and computations
 In Rheology Reviews 2007. British Society of Rheology
, 2007
"... Viscoplasticity is characterized by a yield stress, below which the materials will not deform, and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the HerschelBulkley model, and the Casson model. All of these idea ..."
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Viscoplasticity is characterized by a yield stress, below which the materials will not deform, and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the HerschelBulkley model, and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a continuation parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a cylinder, and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown.
Polymer Rheology: Principles, Techniques and Applications
, 1999
"... Contents Example Problem............................................................................................. i 1. Introduction ..................................................................................................... 1 2. Principles of Rheometry ................................. ..."
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Cited by 2 (1 self)
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Contents Example Problem............................................................................................. i 1. Introduction ..................................................................................................... 1 2. Principles of Rheometry .................................................................................. 3 3. Linear viscoelastic phenomenology.................................................................. 7 4. Approximations used in linear viscoelasticity................................................... 19 5. The viscosity of dilute of polymer solutions and colloidal dispersions .............. 24 6. Linear viscoelastic behavior of concentrated and undiluted polymeric fluids .... 29 7. Nonlinear viscoelastic behavior of concentrated and undiluted polymeric fluids................................................................................................................ 35 8. Straininduced birefringence for concentrated and und
On the Equilibria of the Extended Nematic Polymers under Elongational Flow
, 2007
"... We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples the MaierSaupe shortrange interaction, dipoledipole interaction, and an external elongational flow. We show that all ..."
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We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples the MaierSaupe shortrange interaction, dipoledipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field are axisymmetric. This finding of axisymmetry significantly simplifies any procedure of obtaining experimentally observable equilibria.
Entitled: Nonlinear Vibration Analysis and Optimal Damping Design of Sandwich Cylindrical Shells with Viscoelastic and ERFluid Treatment
, 2012
"... complies with the regulations of the University and meets the accepted standards with respect to originality and quality. Signed by the final examining committee: Chair ..."
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complies with the regulations of the University and meets the accepted standards with respect to originality and quality. Signed by the final examining committee: Chair
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"... Creeping flows of powerlaw fluids through periodic arrays of ..."
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